Problem: Simplify. Remove all perfect squares from inside the square root. $\sqrt{30b^5}=$
Factor $30$ and find the greatest perfect square: $30=2 \cdot 3 \cdot 5$ There are no perfect squares in $30$. Find the greatest perfect square in $b^5$ : $b^5=\left(b^2\right)^2\cdot b$ $\begin{aligned} \sqrt{30b^5}&=\sqrt{30\cdot \left(b^2\right)^2\cdot b} \\\\ &=\sqrt{30} \cdot \sqrt{\left(b^2\right)^2}\cdot \sqrt{b} \\\\ &=\sqrt{30} \cdot b^2\cdot \sqrt{b} \\\\ &=b^2\sqrt{30b} \end{aligned}$